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Séminaire Lotharingien de Combinatoire, B61Ab (2009), 10 pp.

# Bruce E. Sagan

# Probabilistic Proofs of Hook Length Formulas Involving Trees

**Abstract.**
Recently, Han discovered two formulas involving binary
trees which have the interesting property that hooklengths appear as
exponents. The purpose of this note is to give a probabilistic proof
of one of Han's formulas. Yang has generalized Han's results to
ordered trees. We show how the probabilistic approach can also be
used in Yang's setting, as well as for a generalization of Han's
formula in terms of certain infinite trees.

Received: June 11, 2008.
Revised: January 19, 2009.
Accepted: February 22, 2009.

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